基于Julia集的花型图案绘制

Image of flower pattern design based on the Julia set

复数域的非线性映射f(Z)=Z^2+c,是产生分数维图形的一种方法,这种映射能从一种算法中产生出丰富的几何形态——Julia集。由高阶迭代函数f(Z)=Z^m+c,逃逸时间算法及复变函数理论,可推导出高阶Julia集逃逸时间算法,当c取不同的值时,即可绘制出美丽多姿的分形花,且其花瓣数目取决于迭代函数的阶数m,即用m阶迭代函数绘制的分形花呈现出m个花瓣,分形作为一种新颖的图形辅助设计方法,可应用于许多领域。

The nonlinear complex mapping f(Z) = Z2+c is a kind of method to design Fractal image and by one algorithm, which can design very plentiful geometry apearance——Julia set. When c is given different number colorful Fractal flowers can be designed by the high-order interation function f(Z)=Zm + c by the escape time algorithm and the complex function. The numbers of the petals are due to the orders of the interation function, that is, there are m petals of the Fractal flowers with the m-order interation function. Fractal is a novel methods of pattern aided design, which will be applied in many fields extensively.